I've asked this at least twice before but some how I always forget. And the search option has brought up nothing so.

What angle would I have to turn my custom laser beam for each of the 17 frames?

I tried 180/17, but that gave me some huge long decimal number, which I tried, and didn't work anyways, because when I got to frame 8 (or uh... 9 if you're starting from 0 I think) it wasn't completely sideways like other GRP's are when they reach that frame. Unless I did something wrong... I was pretty tired

180/16 = 11.25
The first frame, the one facing "up" is doubled most of the time.

"Doubled"? If you mean what I think you mean, the answer is definitely not. (I assume you mean frame 1 is a duplicate of 0 which is incorrect). I know in Rhino I used a turn difference of 11 or 11.25 at least. I know in max right now HKS set me up a camera system to use for the 17 frames and it's pretty much 100% perfect. If you use max 2009 I can send you the scene.

Frame 8, from 0, is sideways.

I don't think he is modelling at all, Mesk. So he isn't using max or anything.
If you open a ship GRP (at least terrans) you'll see what I mean with doubled frames.
Almost every zergs are doubled too. They aren't really 17 unique frames but 8 only.

That doesn't mean you have to be a lazy bastard as well. None of my grps use duplicate frames of any kind.

Where did I say he has to be lazy?
I can't seem to find that part. In my grps they also have the whole 17 frames but that doesn't change the fact that the turn angle blizzard used is 11.25. Not my fault that blizzard was lazy with some of their grps

I'm just saying. Blizzard always cuts corners.

Blizzard cut corners because they didn't realize people would like UMS and mods so much.